Free vibration of cross-ply piezoelectric laminates in cylindrical bending with arbitrary edges

Based on the piezoelasticity equations for two-dimensional problems, a recently proposed approach, which combines the state-space method and the differential quadrature method, is employed and extended to analyze the free vibration of piezoelectric laminates in cylindrical bending. The application of differential quadrature method to the state equation to approximate the derivatives with respect to the in-plane direction yields a state equation valid at discrete points along that direction. No assumption on deformations and stresses along the thickness direction is introduced, so that the present analysis is very suitable to the analysis of piezoelectric laminates with arbitrary layer-up and thickness. The direct incorporation of standard boundary conditions that are consistent with the basic equations at the two ends into the formulations also avoids the approximation usually introduced if Saint–Venant’s principle is employed. The approach is verified by comparing the results with the exact solution of laminates with simple supports.